In the PN architecture, all features are extracted based only on a single point.
Hence it does not explicitly consider the local neighbourhoods of individual points.
However, local neighbourhoods can contain useful geometric information for pose estimation [1]}.
The local neighbourhoods are considered by an alternative network structure based on the dynamic nearest-neighbour graph network proposed in [2]}.
For each point \(P_i\)  in the point set, a \(k\) -nearest neighbor graph is calculated.
In all our experiments, we use \(k=10\) .
The graph contains directed edges \((i,j_{i1}),\dots ,(i,j_{ik})\) , such that \(P_{j_{i1}},\dots ,P_{j_{ik}}\)  are the \(k\)  closest points to \(P_i\) .
For an edge \(e_{ij}\) , an edge feature \(\begin{bmatrix}P_i, & (P_j - P_i) \end{bmatrix}^T\)  is calculated.
The edge features are then processed in a similar manner as in PointNet to preserve permutation invariance.
This dynamic graph convolution can then be repeated, now calculating the nearest neighbour graph for the feature vectors of the first shared MLP layer, and so on for the subsequent layers.
We use the implementationhttps://github.com/WangYueFt/dgcnn provided by authors from [2]}, and call the resulting network DG for dynamic graph.
